Related papers: Critical Dynamics of Self-Organizing Eulerian Walk…
A new universal {\it empirical} function that depends on a single critical exponent (acceleration exponent) is proposed to describe the scaling behavior in a dissipative kicked rotator. The scaling formalism is used to describe two regimes…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
We study the mean first passage time of a one-dimensional random walker with step sizes decaying exponentially in discrete time. That is step sizes go like $\lambda^{n}$ with $\lambda\leq1$ . We also present, for pedagogical purposes, a…
Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These…
Critical exponents have been obtained for a 3D spin particle system. Clusters are formed and system reaches a critical behavior when fragment size distribution follows a power law, as predicted by Fisher Liquid Droplet Model. Also,…
We study random walks evolving in continuous time on a one-dimensional lattice where each site $x$ hosts a quenched random potential $U_x$. The potentials on different sites are independent, identically distributed Gaussian random…
Consideration is given to the continuous-time supercritical branching random walk over a multidimensional lattice with a finite number of particle generation sources of the same intensity both with and without constraint on the variance of…
The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk with two offsprings. It is shown that two-dimensional…
We revisit the number theoretic division model of self-organized criticality [Phys. Rev. Lett. 101, 158702 (2008)]. The model consists of a pool of $M-1$ ordered integers $\{2, 3, \cdots, M\}$, and the aim is to dynamically form a primitive…
We investigate critical transport and the dynamical exponent through the spreading of an initially localized particle in quadratic Hamiltonians with short-range hopping in lattice dimension $d_l$. We consider critical dynamics that emerges…
We investigate the short time quantum critical dynamics in the imaginary time relaxation processes of finite size systems. Universal scaling behaviors exist in the imaginary time evolution and in particular, the system undergoes a critical…
We study the time evolution of classical spin systems with purely relaxational dynamics, quenched from T >> T_c to the critical point, in the semi-infinite geometry. Shortly after the quench, like in the bulk, a nonequilibrium regime…
Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…
We study self-avoiding walks on three-dimensional critical percolation clusters using a new exact enumeration method. It overcomes the exponential increase in computation time by exploiting the clusters' fractal nature. We enumerate walks…
In this work, we define and calculate critical exponents associated with higher order thermodynamic phase transitions. Such phase transitions can be classified into two classes: with or without a local order parameter. For phase transitions…
The two-terminal conductance of a random flux model defined on a square lattice is investigated numerically at the band center using a transfer matrix method. Due to the chiral symmetry, there exists a critical point where the ensemble…
We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical…
The universal behaviour of the short-time dynamics of the three state Potts model in two dimensions at criticality is investigated with Monte Carlo methods. The initial increase of the order is observed. The new dynamic exponent $\theta$ as…
In this Chapter, we consider a model of $N$ independent random walkers, each of duration $t$, and each starting from the origin, on a lattice in $d$ dimensions. We focus on two observables, namely $D_N(t)$ and $C_N(t)$ denoting respectively…
The eigenvalue spectra of the transition probability matrix for random walks traversing critically disordered clusters in three different types of percolation problems show that the random walker sees a developing Euclidean signature for…